The .380 is a great round for compact guns of you don't mind the recoil of a fixed barrel. There are lots of manufactures that make good guns in .380: Bersa Thunder, Walther PPK, Kel-Tec P3AT, Ruger LCP, S&W Bodyguard, etc. That being said, the .380 kicks hard compared to a 9mm and produces significantly less stopping power.

The guns themselves are more compact then a higher power caliber that requires the barrel to unlock from the slide when it fires (9mm, .40, .45, and so forth). Some of the smaller 9's aren't much bigger then the .380's now and the extra firepower is nice to have in such platforms like the Ruger LC9, Sig P290 or Glock 26 Sub-compact.

Either way being armed with something is better then nothing at all. Best of luck in the search.